Hi Alex! I too prefer hand-drawn maps and am relatively new to it, though hopefully I can still help.
1) In answer to this, I use a 2b pencil to sketch out the maps first, adding some details here and there, but usually not exactly like the final thing. I then use dip pens and pelikan drawing ink to ink them in. I sometimes water some of it down beforehand (but only just started doing that). I have yet to try colouring my maps in ink yet and everything I've done has been a black and white map (and slightly tweaked colours in photoshop). Paperwise, I've been using a rather generic looking A3 drawing pad (it's a little thin perhaps at 120g/m^2) but it gets the job done. Hopefully, I'll get a thicker pad soon, but also have a pad of Bristol Board (250g/m^2) to try out.
Other tools I use are: a ruler (turn it upside to ink with it, or the ink will spread), a rubber for pencil mistakes, several varying nibs (though mainly I just use a slightly thicker one and slightly thinner one), a potractor and set square for marking out, a compass for drawing arcs and circles (though I have nothing to do this with ink other than a steady-ish hand), a pot of water, and a napkin/cloth to wipe down the nibs afterwards.
2) I'm not really sure about the second question yet, having only recently started myself. Only two things really spring to mind, though I'm not really sure if they answer the question properly. One is as I already said, using a ruler turned upside down to ink straight lines. It can take a bit of practice, but gives a much better looking line than I could do freehand. Second is perhaps more general, in that you must always plan out your labels. Remember to leave room for them or bad labelling may ruin a fantastic map. Digitally adding can help with this I guess (I haven't done that), but ultimately if they are not sufficiently planned for, it may just look like a botch job.
I hope this helps and I wish you luck with your mapping endeavours!